I really can't tell the difference between these two. At first I thought that ɐ was something similar to ə, but I'm not sure. I'd appreciate any examples to distinguish these sounds
You can listen to expert IPA pronunciations of the difference here. "Examples" would come from a specific language. As you can see from the Wiki article on the vowel, it is widely transcribed as [ə], but maybe [a]. It does not apparently contrast with [ə] in one language, but may be found in certain dialects instead of [ə]. It may also be conflated with [ɜ]. It is most useful to compare the performance pronunciations of the above-linked experts, since IPA does not specify particular formant values or lexical items in specific languages as representing the value of a given symbol.
If you go to Forvo, you can get over a half million pronunciations of German words. There is a difference between er and e at the end of the word, where final er may be [ɐ]. I don't know of a way to efficiently assemble all of the relevant words, but this is a resource for potentially hearing examples (I'd generally suggest listening to anything with final r). It might be best to pick a single speaker and listen to their pronunciations. Sometimes speakers differ, and you can pick a speaker who has the pronunciation of interest like the first one, and see what similar words there are. Some words are attested with multiple recordings.
1What does this part mean: "It does not apparently contrast with [ə] in one language"? My understanding was that some varieties of German do have a contrast between a phone commonly transcribed [ə] and another phone commonly transcribed [ɐ], e.g. in "eine" [ˈaɪnə] vs. "einer" [ˈaɪnɐ]... Jan 15, 2018 at 21:08
1...although the phonetic details and phonological analysis are not so obvious (German [ə] is typically considered to be an allophone of /ɛ/ in unstressed syllables, and I have heard that in some accents of German, the sound typically transcribed [ə] is in fact closer in quality to [ɛ]; furthermore, I have heard that some native German speakers find that [ɐ] doesn't really sound distinct from German short "a", although this could be because they actually use a not-fully-open quality for "short a") Jan 15, 2018 at 21:09
1I don't know about that variety of German. If these are indeed phonologically distinct as vowel quality, then it would mean that I have to invoke the "apparently" escape, and say "except in German" if it can be established. I'm really not clear what the status of those r's are.– user6726Jan 15, 2018 at 22:19
1Hmm, I thought it was a fairly well-known variety since I see that style of transcription a lot in materials for learners. E.g. this word-reference thread: Pronunciation: -er = -ɐ? and this book German Phonetics and Phonology: Theory and Practice (By Mary Grantham O'Brien, Sarah M. B. Fagan). Jan 15, 2018 at 22:23
1I forgot to mention, [ɐ] is also (often, at least) not considered a phoneme of German: it can be analyzed as /əʁ/ or /ɛʁ/. And actually, what I said earlier about [ə] being analyzed as an allophone of /ɛ/ doesn't actually seem to be done by all phonological analyses, although I don't know why not: users.monash.edu.au/~ewilkins/textbook/CHAP12.PDF Jan 15, 2018 at 22:24